Was Hoping For A Different Differential

(We are in a differential equations class, doing a linear algebra problem. At a late stage of the problem, we are asked to choose random numbers.)

Professor: “Pick a number.”

Student #1: “Three!”

Professor: “Great, now another number.”

Student #2: “Four!”

Professor: “And one more number.”

Student #3: “Five!”

Professor: “Great. Now we plug three, four, and five into the equation to get…”

(The numbers, purely by coincidence, plugged into the equation to get zero, literally the only thing that could have resulted in a solution to the equation.)

Professor: “Oh, you have got to be kidding me…”

(He made us pick the random numbers in the first place to prove the point that the problem cannot be solved for all numbers. When the class realized that we had botched his point by random chance, the whole class burst into laughter.)